M.S.Ramaiah Management Institute, Bangalore | MBA PRIST(A) 2009-11

Presented By

Danny Singh

Karthikey Yamdagini

Krishna Kumar

Kumar Shubham

Monalisa Ghosh

Man Mohan Anand

Introduction

Developed by A.K.Erling in

1903

It analyze the shared facility

needs to be accessed for

service by a large number of

jobs or customers

Examples:

Waiting lines in cafeterias,

hospitals, banks, theaters,

airports etc.

Expected Short Answer Questions

Discussion Slide -1

Define Queuing Model or Queuing Theory

Queuing theory is the mathematical study of waiting lines (or

queues) that enables mathematical analysis of several related

processes, including arriving at the (back of the) queue, waiting in

the queue, and being served by the Service Channels at the front of

the queue.

What do you mean by Traffic Intensity?

The ratio ג/µ is called the traffic intensity or the utilization factor and

it determines the degree to which the capacity of service station is

utilize

)(

)(

RateServiceMean

QueuetheinArrivalofRateMean

Discussion Slide -2

What do you mean by Balking, Reneging, Jockeying?

Balking

If a customer decides not to enter the queue since it is too long is

called Balking

Reneging

If a customer enters the queue but after sometimes loses patience

and leaves it is called Reneging

Jockeying

When there are 2 or more parallel queues and the customers move

from one queue to another is called Jockeying

Discussion Slide -3

What is Waiting Time Cost & Idle Time Cost?

The cost of waiting customers include either the indirect cost of lost

business or direct cost of idle equipment and persons.

The cost of idle service facilities is the payment to be made to the

servers for the period for which they remain idle.

What is Transient & Steady State of the system?

Queuing analysis involves the system’s behavior over time. If the

operating characteristics vary with time then it is said to be transient

state of the system.

If the behavior becomes independent of its initial conditions (no. of

customers in the system) and of the elapsed time is called Steady

State condition of the system

Expected Long Answer Questions

Applications of QM

Queuing Model can be applied to various situations :

Where customers are involved such as restaurants, café,

super market, airports etc.

Very useful in Manufacturing units

Applicable for the problem of machine breakdown & repairs

Applicable for the scheduling of jobs in production control

Applicable for the minimization of traffic congestion at

tollbooth

Provide solution of inventory control problems

Characteristics of Queuing

The basic characteristics of

queuing phenomenon are:

Service Center

Service Channel

Major Constituents of a

Queuing System

Customer

Queue

Service Channel

Customer

Leaving

1

2

3 Waiting Line

Service Facility

System

Customer

Arriving

Elements of Queuing System

Elements of Queuing Models

Arrival Distribution

Service Distribution

Service Channel

Service Discipline

Max. No. of Customer allowed

Calling Source

Customer’s Behavior

Operating Characteristics of QM

Operating Characteristics

of Queuing Models

Queue Length System Length Waiting Time in

the queue Total Time in the system

Utilization Factor

Assumption in Queuing Model

The customer arrive for service at a single service facility at

random according to Poisson distribution with mean arrival rate ג.

The service time has exponential distribution with mean service

rate µ.

The service discipline followed is First Come First Served.

Customer Behavior is Normal

Service facility behavior is Normal

The calling source has infinite size

The mean arrival rate is less than the mean service rate

The waiting space available for customer in the queue is infinite

Limitations of Queuing Model

The waiting space for the customer is usually limited

The arrival rate may be state dependent

The arrival process may not be stationary

The population of customers may not be infinite and the

queuing discipline may not be First Come First Serve

Services may not be rendered continuously

The Queuing system may not have reached the steady state. It

may be, instead, in transient state

References

Books

– Operation Research – D.S.Hira

Websites

– http://en.wikipedia.org

– http://www.google.co.in

– http://www.answers.com

Thank You